On threshold autoregressive processes

By J. Andel, I. Netuka, K. Zvára. 1984

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Citations in the corpus

Semi-analytical approximations to statistical moments of sigmoid and softmax mappings of normal variables (2017, background): “Skewed normal distributions arise in, e.g., stochastic processes that are bounded by an absorbing barrier or threshold (Anděl et al., 1984).”
Some skew-symmetric models (2002, background): “In econometric literature the distribution appears in the so called stochastic frontier model in papers by Aigner et al. (1977), Andel et al. (1984).”
Inference of trends in time series (2007, background): “δu/, where φ and Φ are respectively the standard normal density and normal distribution function (Andel et al., 1984).”
Gaussian Copula Marginal Regression (2012, background): “Secondly, the marginal distribution of the errors is not standard normal anymore but it is the skew-normal distribution [3] with location parameter equal to zero, unit scale parameter and skewness parameter τ/ √ 1− τ2 [1],”
The Skew‐normal Distribution and Related Multivariate Families * (2005, background): “A further related case is the non-linear autoregressive stochastic process studied by Anděl et al. (1984) satisfying a relationship essentially of type Zt ¼ djZt 1j þ ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 d2 p et; t ¼ . . . ; 1; 0; 1; . . . ; Board of the Foundation of the Scandinavian Journal…”
The Second-Order Bias and Mean Squared Error of Estimators in Time Series Models (2007, background): “Andel et al. (1984) showed that the nth moments (about 0) of yt are mn = β −n−1 £2 ¡1− β2¢π¤1/2 Jn, (3.49) where Jn = R +∞ −∞ x ne−kx 2/2Φ (−x) dx, k = β−2−1 (also see Tong, 1990, p. 209).”